Curvature

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Period ending 2026-09-21

6 new papers

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Period ending 2026-09-14

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67 papers

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Beyond Random Couplings: Contrastive Noise Alignment in Generative Flows
Sep 16, 2026Lennart Wittke, Vinicius AzevedoContrastive Alignment Curvature
Right Direction, Wrong Step: Geometric Analysis of Finite-Step Failure in Looped Transformers
Sep 15, 2026Zhihao Guo, Zonghan Wu, Haizhou Du +4Curvature Test-Time Scaling
$\mathbb{SL}(n)$ Representation Learning: An Intrinsic Mixed-Curvature Space with Higher Curvature Capacities and Deeper Order-Aware Composition\mathbb{SL}(n) Representation Learning: An Intrinsic Mixed-Curvature Space with Higher Curvature Capacities and Deeper Order-Aware Composition
Sep 14, 2026Xingrun Li, Yusuke Mukuta, Xin Yang +2Representation Space Hyperbolic Learning
Poisson-Corrector Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling
Sep 14, 2026Yuchen Xin, Zhihua ZhangLangevin Dynamics Lipschitz Constant
Rank-Efficient LoRA via Joint Tangent-Space Optimization under Isotropic Curvature
Sep 14, 2026Zihan Zhu, Zhehang Du, Xuyang Chen +5Low-Rank Adaptation Low-Rank Factorization
Geometric Flow enhanced Graph Coarsening
Sep 14, 2026Chaoqun Fei, Guoxuan Li, Tinglve Zhou +2Graph Neural Networks Riemannian Manifolds
Explaining f-Divergence-Based Regularization via Local Curvature and Sharpness-Aware Minimization
Sep 8, 2026Nour Jamoussi, Marios KountourisBregman Divergences Sharpness-Aware Minimization
Structured Extrema Errors in Classical Surrogates for Viscous Burgers: A Physics-Consistent Interpretation
Sep 7, 2026Youssef OubariSurrogate Models High-Fidelity Surrogates
Beyond the Matrix Sign: Quadratic Spectral Descent
Sep 7, 2026Qiaozhe Zhang, Jun Sun, Yingzhuang LiuMuon Optimizer Muon
Matched Queries for Curvature and Density at Branching Junctions
Sep 1, 2026Ziqi Zhao, Qingjian NiTangent Space Density Ratio Estimation
Hard-ReLU Gradient Descent Selects an Event-Free Sensitivity Limit
Aug 31, 2026Xiaoyang Li, Runni ZhouGradient Flow Curvature
Geometry of Divergence: Tracking Hidden-State Trajectories for Adaptive Multi-Turn Reasoning
Aug 31, 2026Jie Liang, Zhengxin Yu, Hamid Nasiri +1Reasoning Trajectory Multi-Turn Interactions
A Compositional Theory of Curvature in Probabilistic Circuits
Aug 13, 2026Hrithik Suresh, Sahil Sidheekh, Shelar Parth Vijay +3Curvature Sharpness-Aware Minimization
Learning Suffers More Than the Policy Class Under Partial Observability: A Closed-Form Analysis
Aug 7, 2026Idil GözelSoft Actor-Critic Deep Reinforcement Learning
Edge Sparsification via Temporal Forman-Ricci Curvature for Dynamic Graph Learning
Aug 7, 2026Poupak Azad, Cuneyt Gurcan Akcora, Kiarash ShamsiTemporal Graphs Curvature
Understanding Differentiable Embeddings Through Differential and Integral Geometry
Aug 7, 2026Xinyu Zhang, Klaus MuellerEmbedding Dimension Curvature
MALT: Lightweight Curvature-Aware Muon via Diagonal Preconditioning
Aug 5, 2026Tongle Wu, Huanyu Dong, Ying Sun +1Curvature-Aware Quadratic Banks Spectral Preconditioning
Quotient Dynamics, Effective Curvature, and Implicit Bias in Positive Quadratic Networks
Jul 28, 2026Pengcheng ChengCurvature Wasserstein Gradient Flows
Guiding Posterior Exploration with Optimizer-Derived Geometry
Jul 28, 2026Moritz Schlager, Emanuel Sommer, Thomas Möllenhoff +1Bayesian Neural Networks Bayesian Optimization
PointCHR: Point Cloud Analysis via Curvature-Aware Hyperbolic Rectification
Jul 27, 2026Xinxing Yu, Liying Yang, Hao Mo +4Certified Point-Cloud Hyperbolic Space
Distribution-Specific Curvature Control with Finite-Sample Guarantees for Open-Weight Safety
Jul 24, 2026Domenic Rosati, Ali Dadsetan, Hong Huang +5Harmful Fine-Tuning Safety Alignment
Learning from the Descent Direction: Adaptive Gradient Descent under One-Sided Hölder Regularity
Jul 24, 2026Arzu Ahmadova, Ismail HuseynovGradient Descent Descent
Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature
Jul 24, 2026Rachid Caich, Yassine AbbahaddouGraph Neural Networks Curvature
Decentralized Online Riemannian Optimization for Strongly Geodesically Convex Functions
Jul 22, 2026Zhanyuan Cai, Emre Sahinoglu, Shahin ShahrampourRiemannian Optimization Convex Sets
The Price of Hidden Curvature: An $\widetildeΩ (d^{5/4} \sqrt{T})$ Lower Bound for Bandit Convex OptimizationThe Price of Hidden Curvature: An \widetildeΩ (d^{5/4} \sqrt{T}) Lower Bound for Bandit Convex Optimization
Jul 21, 2026Nived RajaramanO(T^Β)$ Simultaneous Regret Convex Optimization
The Curvature Shadow: An Apparent Failure of Maximum-Entropy Equilibrium Selection is a Removable Artifact
Jul 20, 2026Luis LealNash Equilibrium Entropy-Regularized Equilibrium Selection
Discrete Ricci Curvature on Protein Contact Graphs for Lightweight Fold Classification
Jul 17, 2026Jianru ShenEmbedding Dimension Rotation-Invariant Descriptors
Gradient-Energy Guided Block-Wise Perturbations for Sharpness-Aware Minimization
Jul 17, 2026Zhen Huang, Jiaxin Deng, Junbiao PangSharpness-Aware Minimization Curvature
Partial Identification with Multiple Nonlinear Measurements of a Latent Regressor
Jul 13, 2026Burhan Ogut, Michelle YinStructural Equation Models Latent Variable
Higher-Order Geometric Updates for Levenberg-Marquardt Method via Riemann Normal Coordinates
Jul 8, 2026Jianing Liu, Dong H. ZhangRiemannian Optimization Least Squares
Leveraging Extragradient for Effective Sharpness-Aware Minimization in Deep Learning
Jul 7, 2026Yao Fu, Chunxia Zhang, Junmin Liu +3Stochastic Gradient Descent Sharpness-Aware Minimization
Differentially Private Natural Gradient Descent
Jul 7, 2026Pan Li, Kai Chen, Shuai Chang +3Differential Privacy Stochastic Gradient Descent
Is the Geometry Doing the Work? An Operating-Point Audit of Hierarchy in Hyperbolic Vision-Language Models
Jul 6, 2026Jaeyoung Kim, Eunseok Kim, Dongsuk JangRepresentational Geometry Large Vision Language Models
Curvature-Guided Sheaf Diffusion for Unsupervised Community Detection on Heterophilic Graphs
Jun 29, 2026Feifan WangText-Attributed Graph Curvature
Characterizing Optimizer-Dependent Training Dynamics Through Hessian Eigenvector Displacement and Localization
Jun 29, 2026Marcelina Marjankowska, Valerio Modugno, Paolo BaruccaCondition Number Curvature
Knowing in Advance When an Evolutionary Outer Loop Will Not Help: A Pre-Registered Cheap-Baseline Screening Rule
Jun 28, 2026Ramchand KumaresanScreening Early Stopping
Adaptive Iterative Hard Thresholding for Online High-dimensional Quantile Regression
Jun 26, 2026Zitian Zhou, Nan LinQuantile Regression Learning-Augmented Algorithms
Spectral Perturbation of the Empirical Fisher Information Matrix under Weight Quantization
Jun 26, 2026Rahid Zahid Alekberli, Hikmat KarimovFisher Information Quantization
A Single Stepsize Suffices for Unprojected Linear TD(0): Simultaneous Robust and Fast Rates via Polyak--Ruppert Averaging
Jun 23, 2026Wei-Cheng Lee, Francesco OrabonaLarge Step Sizes Markovian Sampling
Ramanujan Graph Rewiring with Non Negative Resistance Curvature
Jun 19, 2026Hugo Attali, Rachid El JouhriGraph Neural Networks Curvature
Learned Radius Estimation for UDF-Based Point Cloud Reconstruction
Jun 17, 2026Eito Ogawa, Hiroshi WatanabeCurvature
Computing Smooth Geodesics under Two-Sided Curvature Bounds with Applications to Robotics and Image Analysis
Jun 11, 2026Da Chen, Zhenjiang Li, Jean-Marie Mirebeau +4Geodesic Curvature
The Post-GCN Decade Revisited: Curvature-Stratified Evaluation of Relational Learning
Jun 4, 2026Shuo Wang, Xiangyu Wang, Quanxin Wang +9Relational Deep Learning Graph Neural Networks
Waypoints Matter: A Systematic Study for Sampling-Based Trajectory Planning
Jun 4, 2026Josep M. Barbera, Antonio Artuñedo, Jorge VillagraAutonomous Driving Trajectory Prediction
Efficient Mean Curvature Computation on High-Dimensional Data Manifolds
Jun 4, 2026Alexandre L. M. LevadaCurvature Covariance Estimation
Why Muon Outperforms Adam: A Curvature Perspective
Jun 3, 2026Shuche Wang, Fengzhuo Zhang, Jiaxiang Li +2Adam Muon
MAdam: Metric-Aware Multi-Objective Adam
Jun 2, 2026Fengbei Liu, Rachit Saluja, Sunwoo Kwak +5Adam Multi-Objective Optimization
Beyond $\ell_2$ -norm and $\ell_\infty$ -norm: A Curvature-Inspired $\ell_p$ -Norm Scheme for Deep Neural NetworksBeyond \ell_2-norm and \ell_\infty-norm: A Curvature-Inspired \ell_p-Norm Scheme for Deep Neural Networks
Jun 1, 2026Jianhao Xu, Zhuang YangNeural Network Optimization Stochastic Gradient Descent
Don't Read Everything: A Curvature-Conditioned Query for Linear Attention
May 31, 2026Dong Le, Thong Nguyen, Cong-Duy Nguyen +1Quadratic Attention Efficient Long-Context Inference
hZACH-ViT: Curved Latent Geometry for Compact Vision Transformers in Low-Data Medical Imaging
May 30, 2026Athanasios AngelakisSelf-Supervised Vision Transformers Vision Transformer
Exploiting weight-space symmetries for approximating curvature
May 30, 2026Artem Artemev, Rui Xia, Benjamin M. Boyd +4Curvature Condition Number
Geodesics with Unified Tangent-constrained Priors and Curvature Regularization
May 28, 2026Chong Di, Li Liu, Jinglin Zhang +3Geodesic Curvature
Localizing Memorized Regions in Diffusion Models via Coordinate-Wise Curvature Differences
May 26, 2026Gwangho Kim, Sungyoon LeeCurvature Localization Methods
Spectral Asymptotics of Neural Network Loss Landscapes: An Exact Decomposition of the Curvature Exponent
May 22, 2026Anherutowa CalvoCondition Number Curvature
Why Zeroth-Order Adaptation May Forget Less: A Randomized Shaping Theory
May 11, 2026Yao Shu, Jian Mu, Zhongxiang DaiZeroth-Order Optimization Catastrophic Forgetting
Curvature Beyond Positivity: Greedy Guarantees for Arbitrary Submodular Functions
May 8, 2026Yixin Chen, Alan KuhnleSubmodular Maximization Curvature
KANs need curvature: penalties for compositional smoothness
May 4, 2026James BagrowKolmogorov-Arnold Networks Curvature
MTCurv: Deep learning for direct microtubule curvature mapping in noisy fluorescence microscopy images
Apr 29, 2026Achraf Ait Laydi, Sidi Mohamed Sid'El Moctar, Yousef El Mourabit +1Microscopy Curvature
Representational Curvature Modulates Behavioral Uncertainty in Large Language Models
Apr 27, 2026Jack King, Evelina Fedorenko, Eghbal A. HosseiniLarge Language Model Uncertainty Next-Token Prediction
Quasi-Quadratic Gradient: A New Direction for Accelerating the BFGS Method in Quasi-Newton Optimization
Apr 27, 2026John ChiangNewton Proximal Gradient Descent

Sep 16, 2026 · cs.CVJ/K move · Enter open · S save

Beyond Random Couplings: Contrastive Noise Alignment in Generative Flows

Lennart Wittke, Vinicius Azevedo

Diffusion and flow-matching models are typically trained by corrupting data through independently sampled Gaussian noise. While simple and scalable, this forward process induces arbitrary data-noise couplings, forcing the network to learn high-curvature transports between unrelated endpoints. Existing optimal-transport methods reduce this burden by reassigning fixed noise samples to data, but the source noise distribution itself remains passive. To address this, we introduce Contrastive Noise Alignment (CNA), a training-time method that creates dynamic, contrastive couplings by optimizing the noise representations directly. By modeling the noise batch as an interacting particle system, CNA employs a cross-modal InfoNCE objective to align noise particles with their paired data targets. To prevent spatial collapse, this alignment is regularized using an angular entropy term and a radial norm penalty. We show theoretically that this equilibrium asymptotically preserves Gaussian structures, maintaining tractability during inference. Empirically, CNA improves the alignment between noise and data, reduces flow curvature, and provides better generation quality with fewer required sampling steps. For few-step, pixel-space generation (2-4 NFEs), CNA reduces FID by over 50% compared to standard rectified flow, and by at least 24% against Optimal Transport baselines.

Contrastive Alignment Curvature

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